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« Maintenance »

expertise

UPSTREAM ACTIVITIES- Management

- Programs, Preparation

- Logistics support management

- Organisation, tasks monitoring

- Budgetary control

- Administration

DOWNSTREAM

ACTIVITIES- Experience follow-up

- Indicators

- Diagnostic maintenance

- Benchmarking

- Improvement process

- …

RoboticsSurveillance

and control

approaches

RealizationMaintenance

CorrectivePreventive

Scheduled On Condition

Maintenance: definition

Group of technical, administrative and managerial actions during one component’s life

cycle, intended to keep or re-establish it into a state which allows it to carry out the

required functions [EN13306]

Strategy setting

• Maintenance Management Process

Strategy Definitionconditions the success of maintenance in an organization,

determines the effectiveness of the subsequent implementation

Strategy Implementationallow us to minimize the maintenance direct cost,

determines the efficiency of our management

Strategy setting






“…doing the right thing”

Strategy setting






“…doing the right thing”

“…doing the (right) thing right”

Maintenance Decision-Making Strategies: the issue

• Industrial systems are made up of various components,equipment and structures characterized by:– different reliability– different failure mechanisms– different impacts on the cost of operation– different impacts on the safety of the equipment, operators and public

• Each equipment needs to have a maintenance approach that is appropriate toits characteristics and to the consequences of its failure.

• A decision must be taken on the maintenance strategy, which defines thecomponents of a system that will have a corrective, scheduled or condition-based maintenance and will further specify the details of each of this type ofapproaches

What to take into account, for every component?

LegislationCompany’s

quality policy

Manufacturer

indications

Maintenance

experience

Job priority

analysis

Criticality

analysis

Mathematical

models

Component

Work instruction description

Required disciplines

Required working hours and spare list

Eventual priorities

Unplanned

Periodic

Condition-based

Predictive

…

Maintenance Strategy

• Reliability-Centred Maintenance (RCM)

• Risk-Based Maintenance (RBM)

Two common approaches for defining a maintenance strategy

Maintenance Strategy

Two common approaches for defining a maintenance strategy

• Reliability-Centred Maintenance (RCM)

• Risk-Based Maintenance (RBM)

Risk-Based Maintenance (RBM)

• BASIC IDEA: Risk is the criterion for the basis of maintenance planning.

• OBJECTIVE: reduce the overall risk that may result as the consequence of unexpected failures of operating facilities.

• METHOD: – Identify all the failure scenarios– Determine the associated risk– Prioritize the failure scenarios according to the associated risk– Develop a maintenance strategy that minimizes the occurrence of the

high-risk failure scenarios:

• EXPECTED RESULTS: high-risk components will be inspected with greater frequency and maintained in a more thorough manner, so that the overall operation of the system achieves tolerable risk criteria.

The Concept of Risk

Hazard

Environment

People

The Concept of Risk

Hazard

Safeguards

Environment

People

The Concept of Risk

Hazard

Safeguards

Environment

People

UNCERTAINTY

Risk Analysis: scenario

Accident

Scenarios

Identification

QualitativeRAM

analyses

1. What undesired conditions may occur? Accident Scenario, S

Hazard Analysis

Hazop

FMEA


2. With what probability do they occur? Probability, p

Failure

Probabilty

Assessment

FTA

ETA

Markov Models

Hazard Analysis

Hazop

Accident

Scenarios

IdentificationFMEA

QuantitativeRAM

analyses

QualitativeRAM

analyses

Petri Net

Bayesian Networks

Risk Analysis: probability

Uncertainty Representation: (probabilistic & non-probabilistic frameworks)

Uncertainty Propagation (advanced and hybrid MC methods)

Multi-state degradation modelsDynamic behaviors

Influencing Factors


2. With what probability do they occur? Probability, p

3. What damage do they cause? Consequence, x

Failure

Probabilty

Assessment

FTA

ETA

Markov Models

Hazard Analysis

Hazop

Accident

Scenarios

IdentificationFMEA

QuantitativeRAM

analyses

QualitativeRAM

analyses

Petri Net

Bayesian Networks Evaluation of

the

consequences

International Standards

Best Practices & Lessons Learnt

Transport Model

Resilience and Vulnerability analysis

Risk Analysis: consequence

Fire& Explosion models

ABM for Emergent phenomena




Influencing Factors

Failure

Probabilty

Assessment

FTA

ETA

Markov Models

Hazard Analysis

Hazop

Accident

Scenarios

IdentificationFMEA

QuantitativeRAM

analyses

QualitativeRAM

analyses

Petri Net


the

consequences

RISK = {Si, pi, xi}

4

3

2

1

p/x A B C D

Risk Analysis: evaluation



Transport Model







Influencing Factors

Failure

Probabilty

Assessment

FTA

ETA

Markov Models

Hazard Analysis

Hazop

Accident

Scenarios

IdentificationFMEA

QuantitativeRAM

analyses

QualitativeRAM

analyses

Petri Net


the

consequences




Transport Model




Risk mitigationMa

inte

nan

ce

De

sig

n

PHM

Inspections

FRACAS/RCA

Redundancies

Reliable components




Influencing Factors

Failure

Probabilty

Assessment

FTA

ETA

Markov Models

Hazard Analysis

Hazop

Accident

Scenarios

IdentificationFMEA

QuantitativeRAM

analyses

QualitativeRAM

analyses

Petri Net


the

consequences




Transport Model







Influencing Factors

Risk mitigationMa

inte

nan

ce

De

sig

n

PHM

Inspections

FRACAS/RCA

Redundancies

Reliable components

How to cost-effectively

reduce the asset risk?

Risk-Based Maintenance: techniques

1. Risk Assessment

2. Maintenance planning based on risk:• Maintenance should be planned so as to lower the risk to meet the acceptable

criterion by reducing the probability of failures and their consequences

• Typical approaches for decision-making used are:

- the Reverse Fault Tree Analysis (RFTA): assign the desired probability of the topevent (failure scenario) such to satisfy the acceptable risk criterion; compute thecorresponding new probabilities of the basic events (failure modes) and fromthese infer the corresponding maintenance intervals;

- the Analytic Hierarchy Process (AHP): identify the risk factors affecting thefailure scenario; pairwise compare their importance in contributing to the failurescenario; derive the risk factors likelihoods; combine the risk factors likelihoods tocompute the probability of failure; prioritize components and plan maintenanceinterventions based on the risk factors likelihood contributions and relatedinsights.

Reverse Fault Tree Analysis

21

Example: CANDU airlock system

The Airlock System (AS)

prevents the dispersion of

contaminants by keeping

the pressure of the inside

of the reactor vault lower than the outside pressure.

Basic Failure Events ID Code

1Pressure equalizer valve

failureV1

2 Doors failure D1

3 Seal failure S1

4 Gearbox failure G1

5 Minor pipe leakages P1

6 Major pipe leakages P2

7 Exhaust pipe failure E1

8 Empty tank T1

9 Tank failure T2

Lee A., Lu L., “Petri Net Modeling for Probabilistic Safety Assessment and its

Application in the Air Lock System of a CANDU Nuclear Power Plant”, Procedia

Engineering, 2012 International Symposium on Safety Science and Technology,

Volume 25, pp.11-20, 2012.

Fault Tree Model

Objective: Reduce the Top Event probability to make the risk acceptable

Decision Problem: how?

Top event = “AS fails to maintain the

pressure boundary”.

FT developed for

analyzing a scenario of

a Design Basis Accident

occurred in the AS of a

CANDU Nuclear Power

Plant in 2011.

‘Traditional’ RFTA Approach

Application of Risk Importance Measures (RIMs), which aim at quantifying the

contribution of components or basic events to the system risk

Example: Risk Reduction Worth (RRW) is the maximum decrease in risk

consequent to an improvement of the component associated with the basic failure

event considered

𝑅𝑅𝑊𝐷𝑜𝑜𝑟 =𝑃(𝐴𝑖𝑟 𝐿𝑜𝑐𝑘 𝐹𝑎𝑖𝑙𝑢𝑟𝑒)

𝑃(𝐴𝑖𝑟 𝐿𝑜𝑐𝑘 𝑓𝑎𝑖𝑙𝑢𝑟𝑒|𝐷𝑜𝑜𝑟 𝑤𝑜𝑟𝑘𝑖𝑛𝑔)






event considered

Approach (Iterative):

Rank component importance values

Calculate component RRW values

Apply one of the possible actions on the most important basic

event






event considered

Approach (Iterative):

Rank component importance values

Calculate component RRW values

Apply one of the possible actions on the most important basic

event

Drawback:the procedure does not

necessarily lead to the global

optimal solution

27

• Objectives

– Develop methods for identifying combinations (portfolios) of risk management actions to minimize residual risks at different cost levels of risk management cost

– Account for risk, cost of risk management and resource constraints simultaneously

– Apply and evaluate methods to nuclear and other safety critical systems

• Challenges

– Develop computationally tractable approaches for large systems

– Using incomplete information when reliable parameter estimates are not available

Portfolio Optimization for RBM

28

Methodology steps:

1. Failure scenario modeling

2. Definition of failure probabilities

3. Specification of actions

4. Optimization model

Our methodology

29

Reference: Khakzad N., Khan F., Amyotte P., Dynamic safety analysis of process systems by mapping bow-tie into

Bayesian network, Process Safety and Environmental Protection 91 (1-2), pp. 46-53 (2013).

To analyze the failure

scenarios, the Fault Tree is

mapped into a Bayesian Belief

Network.

Step 1: Failure scenario modeling

30

Step 1: Airlock system failure modeling

Multi-state description

of pipe leakage event

Advantages of BBN

Multi-state modeling

Step 1: Airlock system failure modeling

Advantages of BBN

Multi-state modeling

Extension of concepts of AND/OR gates

Example: AND gate

32

Information sources

• Information provided by AND/OR gates in FT

• Statistical analyses

• Expert elicitation

The probability of occurrence of the events is defined according to their role in the failure scenarios. Specifically:

• Initiating events failure probabilities of system components;

• Intermediate and top events conditional probability tables.

Step 2: Definition of failure probabilities

Step 3: Specification of actions

Action characteristics:

• Impact on the prior and conditional probabilities;

Action 𝑎 modify the probability of occurrence of the states 𝑠 of event 𝑖.

𝑠

𝑃𝑖(s)

𝑠

𝑃𝑎𝑖(s)

Step 2 and 3: Definition of failure probabilities

Action RRR

Calibration test 𝑎1 10−1

Sensor 𝑎2 10−2

Valve failure

𝑃𝑎12 𝑠 = 1 = 10−4 ∙ 10−1

𝑃𝑎22 𝑠 = 1 = 10−4 ∙ 10−2

Risk Reduction Rate

(RRR)

Step 3: Specification of actions

Action characteristics:

• Impact on the prior and conditional probabilities;

• Entail a cost (capital investment costs and ordinary periodic expenses over the life-time). To consider this, we relay on the annualized cost at year Λ (time horizon):

• r= discounted rate, 𝜆=year number

36

Action Parameters

Synergic

effect:

selection of

both

actions

cost saving

and risk

reduction

extra-benefit

37

Actions Parameters

Synergic

effect: if we

act on both

seal and pipe,

we gain a cost

saving

Step 4: Optimization model

Risk

acceptability

Sele

ct th

e o

ptim

al a

ctio

n p

ortfo

lio

Action portfolio #2

Action portfolio #3

Action portfolio #4

Action portfolio #5

Action portfolio #9

Budget

constraints

Action

feasibility

Implicit enumeration algorithm to

identify the optimal portfolios of

safety actions.

The resulting portfolios are

globally optimal in the sense that

minimize the failure risk of critical

events, instead of selecting

actions that target the riskiness of

the single events.

Action portfolio #6

Action portfolio #7

Action portfolio #8

Action portfolio #10



Action portfolio #1

Step 4: Optimization model results

Airlock failure probability for the

optimal portfolio of actions for different

budget levels.

Greater budget more effective

actions lower residual risk of failure

of the airlock system.

Step 4: Optimization model results

Application of RRW approach

The application of this approach leads to the following issues

Iteration Most risky event Issue

𝑡 = 1 Valve failureThere are two possible actions, so which one

should the experts select?

𝑡 = 2 Tank failureThe only applicable action is very expensive, could it be that many inexpensive actions have a higher

impact on risk reduction?

𝑡 = 3Valve failureDoor failure

In case of a limited budget, which componentshould be improved first?

𝑡 = 4 Valve failureIf the experts apply a second action, do the joined

actions have the same characteristics as two separate actions?

45

• If we are given Budget B=350K€, then we getthe following results:

Final Comparison

Application of Risk Importance Measures (RIMs)

Limitations of using RIM for RFTA in RBM:

• Actions can be applied to initiating events only not accounting for synergies of joined actions.

• They do not account for feasibility and budget constraints.

• They do not necessarily lead to the global optimal portfolio of actions because the procedure implies assumptions and expert opinions which strongly affect the decisions at the following iterations.

• They cannot be applied in case of multi-state and multi-objective failure scenarios they account for a unique critical event.

Application of AHP to RBM

47

48

• A multiple criteria decision-making technique, which allows toreduce complex decisions to a series of simple comparisonsand rankings

• It is used in RBM applications to prioritize components andplan maintenance interventions based on the risk factorslikelihood and consequence contributions, and relatedinsights

AHP: What is it?

49

• Phase 1: formulate the decision problem in the form of ahierarchical structure. The decomposition of the decisioncriteria proceeds until further refinements are not needed.

– Top level: overall objective of the decision problem

– Intermediate levels: elements affecting the decision

– Lowest level: decision options

AHP: Method

50

• Crude oil pipeline (1500 km) in the western part of India.

• The entire pipeline is classified into a few (in this case 5) stretches (i.e.,pipeline sections in between two stations).

• A risk structure model is built in the Analytic Hierarchy Process (AHP)framework.

Example

P.K. Dey, A risk-based maintenance model for inspection and maintenance of cross-country petroleum pipeline, J.

Qual. Maint. Eng. 7 (1) (2001), 25–41.

51


• Phase 2: determine the relative importance of the elements in each level of the hierarchy through a pair-wise comparison. Each element in an upper level of the hierarchical tree is used as criterion to compare the elements in the level immediately below.

AHP: Method

how many times more

important or dominant an

element is over another

Intensity of

Importance

Definition Explanation

1 Equal Importance Two activities contribute equally to the objective

3 Moderate importance Experience and judgment slightly favor one activity over another

5 Strong importance Experience and judgment strongly favor one activity over another

7 Very strong or demonstrated

importance

An activity is favored very strongly over another; its dominance

demonstrated in practice

9 Extreme importance The evidence favoring one activity over another is of the highest

possible order of affirmation

2,4,6,8 For compromise between the above

values

Sometimes one needs to interpolate a compromise judgment

numerically because there is no good word to describe it.

52

• Pairwise comparisons of risk factors

• Each number represents the expert’s view about the dominance of the element in the column on the left over the element in the row on top.

Example

Slightly favours of Corrosion over external interference

Dominance of corrosion over Acts of God

demonstrated in practice

53


• Phase 2: determine the relative importance of the elements ineach level of the hierarchy through a pair-wise comparison.Each element in an upper level of the hierarchical tree is usedas criterion to compare the elements in the level immediatelybelow.

• Phase 3: compute the relative weights of the factors(mathematical procedure based on eigenvectorscomputation)

AHP: Method

54

Example

Preference

Weight

55


• Phase 2: determine the relative importance of the elements ineach level of the hierarchy through a pair-wise comparison.Each element in an upper level of the hierarchical tree is usedas criterion to compare the elements in the level immediatelybelow.

• Phase 3: compute the relative weights of the factors(mathematical procedure based on eigenvectorscomputation)

• Phase 4: compute the relative weights of the alternatives withrespect to the leaves of the tree

• Phase 5: find the composite weights of the decisionalternatives by aggregating the weights through hierarchy.

AHP: Method

56

Example

Final weights

Final ranking

57

• AHP limitations:– the rank reversal phenomenon (i.e., the relative ranking of

two alternatives may change when a new alternative is introduced)

– Shortcomings of the 1-9 ratio scale

– Pitfalls in quantification of qualitatively stated pairwise comparisons

– Not applicable in case of a large number of alternatives

– Uncertainty is not accounted

• The AHP-based RBM methodology does not tackle the problem of how to optimize the inspection campaign

Methodology drawback

58

The objective

•Develop a methodology to select portfolios of maintenance inspections to optimally allocate resources to minimize costs and maximize the benefit of maintenance on risk reduction

• Accomodate imprecision of expert judgments

59

Proposed method

Failure likelihood and severity assessment

• criticality ranking of items

Item-specific maintenance optimization

• item’s condition-specific rule to select maintenance option

Maintenance portfolio

optimization

• proposal for maintenance resources allocation

60

Proposed method






optimization


61

Multi Attribute Value Theory

Likelihood

Pipe Features

Material Pipe Age Diameter

Past Events

Blockages Flushing

Local Circumstances

Soil Traffic Load

Step 1: Value treeOperational

losses

Item repair cost

Cost to externals

62


Step 1: Value tree

Step 2: Score elicitation for leaf attributes (SWING Method)

Likelihood

Pipe Features


Past Events

Blockages Flushing

Local Circumstances

Soil Traffic Load

൧𝑣𝑖 𝑥𝑖𝑗

= [𝑣𝑖 𝑥𝑖𝑗; 𝑣𝑖(𝑥𝑖

𝑗)

𝑖=leaf attribute

𝑥𝑖𝑗=score of pipe 𝑗 with respect to attribute 𝑖

63

Example

0

20

40

60

80

100

120

1940 1960 1980 2000 2020

Sco

re

Pipe age

Elicited Expert Preferences

«The installation year before 1955 has the maximum influence on Pipe features»

«If the installation year is 1985, its influence on Pipe Features is between 40 and

80% of that of 1955»

64


Likelihood

Pipe Features


Past Events

Blockages Flushing

Local Circumstances

Soil Traffic Load

Step 1: Value tree

Step 2: Score elicitation for leaf attributes (SWING Method)

Step 3: Criteria relative importance (PAIRS Method)

65

Example

«With resepect to 𝑝𝑖𝑝𝑒 𝑓𝑒𝑎𝑡𝑢𝑟𝑒, attribute 𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 is more important than attribute 𝐴𝑔𝑒 which in turn is more important than attribute 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟».

𝑤𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 ≥ 𝑤𝐴𝑔𝑒 ≥ 𝑤𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟

𝑤𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 + 𝑤𝐴𝑔𝑒 + 𝑤𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 = 1

Diameter

Age

Material

Feasible

region

𝑣𝑝𝑖𝑝𝑒 𝑓𝑒𝑎𝑡𝑢𝑟𝑒 𝑥𝑗 = min[

𝑖

𝑤𝑖 𝑣𝑖 𝑥𝑖𝑗]

𝑣𝑝𝑖𝑝𝑒 𝑓𝑒𝑎𝑡𝑢𝑟𝑒 𝑥𝑗 = max[

𝑖

𝑤𝑖 𝑣𝑖(𝑥𝑖𝑗)]

Under mild assumptions, the

maximum and minimum values are

attained at the extreme points of the

weight feasible region (i.e.,

1 0 0 ;1

2

1

20 ; (

1

3

1

3

1

3))

𝑣𝑝𝑖𝑝𝑒 𝑓𝑒𝑎𝑡𝑢𝑟𝑒 𝑥𝑗 = min[1 ∙ 𝑣𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑥𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑗

,1

2𝑣𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑥𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙

𝑗+1

2𝑣𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑥𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟

𝑗,1

3𝑣𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑥𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙

𝑗+1

3𝑣𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑥𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟

𝑗+1

3𝑣𝐴𝑔𝑒 𝑥𝐴𝑔𝑒

𝑗]

66

𝑙=first level attribute

Back-propagation of uncertainty

𝑤𝑝𝑖𝑝𝑒 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑠 ≥ 𝑤𝑙𝑜𝑐𝑎𝑙 𝑐𝑖𝑟𝑐𝑢𝑚𝑠𝑡𝑎𝑛𝑐𝑒𝑠

𝑤𝑝𝑎𝑠𝑡 𝑒𝑣𝑒𝑛𝑡𝑠 ≥ 𝑤𝑙𝑜𝑐𝑎𝑙 𝑐𝑖𝑟𝑐𝑢𝑚𝑠𝑡𝑎𝑛𝑐𝑒𝑠Pipe Features

Past events

Local Circumstances

Feasible

region

Example: Elicited Expert Preferences

«Local circumstances is the least important criterion in defining pipe failure

likelihood»

• 𝑣𝐿 𝑥𝑗 = min[σ𝑙𝑤𝑖 𝑣𝑖 𝑥𝑖𝑗]

• 𝑣𝐿 𝑥𝑗 = max[σ𝑙𝑤𝑖 𝑣𝑖(𝑥𝑖𝑗)]

67


Likelihood

Pipe Features


Past Events

Blockages Flushing

Local Circumstances

Soil Traffic Load

Step 1: Value tree

Step 2: Criteria relative importance

Step 3: Score elitation for leaf attributes

Step 4: Value computation

Material Pipe Age Diameter Blockages Flushings Soil Traffic Load Likelihood

Pipe ID1 [30 40] [10 20] [100 100] [40 60] [50 60] [20 40] [30 50] [40 60 ]

Pipe ID2 … …. …

….

Feasible criteria weights

Back-p

ropagaio

no

f

uncerta

inty

68

Risk Assessment

Dominance Non Dominance

Item 𝒙𝒕

Material: concrete

Pipe Age: 10 years

…

Likelihood score: [20 40]

Severity score: [30 60]

Item 𝒙𝒋

Material: PVC

Pipe Age: 40 years

…



Item 𝒙𝒌

Material: cast iron

Pipe Age: 30 years

…



𝒙𝒕

𝒙𝒋 𝒙𝒋

𝒙𝒌

69

Risk Assessment: Output

Pareto front of most

critical maintenance items

Item 3

Item 56

Item 72

Item 101

…

…

…

70

Proposed method






optimization


71

Decision Tree Analysis

The benefit of performing maintenance depends on the item degradation state

These can be uncertain

72


The benefit of performing maintenance depends on the item degradation state.

The probability of being in state 𝑠 depends on the pipe likelihood and is uncertain

Degrad

ation

State

𝑝𝑠𝑑 𝑝𝑠

𝑑

𝑠 = 1 0 0.3

𝑠 = 2 0.3 0.5

𝑠 = 3 0.4 0.6

𝑠 = 4 0.5 0.7

𝑠 = 5 0.6 0.8

𝑠 = 6 0.7 0.9

73


൧𝑐𝑗𝑡 = [𝑐𝑗

𝑡; ҧ𝑐𝑗𝑡

𝑐𝑗𝑠; ҧ𝑐𝑗

𝑠

𝑐𝑗𝑑; ҧ𝑐𝑗

𝑑


𝑑


𝑑

We estimate the interval-valued costs of inspection, renovation and disruption

74





𝑠


𝑑


𝑑


𝑑

Lower bound cost of renovation 𝐶renj

(𝑠) = 𝑐𝑗𝑑 ∙ 𝑝1

𝑑 + 𝑐𝑗𝑠

Upper bound cost of renovation 𝐶renj

(𝑠) = ҧ𝑐𝑗𝑑 ∙ 𝑝

1𝑑+ ҧ𝑐𝑗

𝑠

75





𝑠


𝑑


𝑑


𝑑

Lower bound cost of no renovation 𝐶NOrenj

(𝑠) = 𝑐𝑗𝑑 ∙ 𝑝𝑠

𝑑

Upper bound cost of no renovation 𝐶NOrenj

(𝑠) = ҧ𝑐𝑗𝑑 ∙ 𝑝

𝑠𝑑

76





𝑠


𝑑


𝑑


𝑑

We will decide to renovate pipe 𝑗 only if 𝐶renj

𝑠 < 𝐶NOrenj

(𝑠)

77





𝑠


𝑑


𝑑


𝑑

The benefit of inspetion is related to the reduction of expected disruption cost

𝐵𝑗𝑠 =

0 if optimal decision is NO ren

𝐶NOrenj

(𝑠) − 𝐶renj

(s) otherwise

78





𝑠


𝑑


𝑑


𝑑

The benefit of inspetion is related to the reduction of expected disruption cost

ത𝐵𝑗𝑠 =

0 if optimal decision is NO ren

ҧ𝐶NOrenj

(𝑠) − 𝐶renj

(s) otherwise

79





𝑠


𝑑


𝑑


𝑑

Expected Benefit 𝐵𝑗 =

𝑠∈𝑆

𝑝𝑗𝑠 ∙ 𝐵𝑗

𝑠 ത𝐵𝑗 =

𝑠∈𝑆

𝑝𝑗𝑠 ∙ ത𝐵𝑗

𝑠

80





𝑠


𝑑


𝑑


𝑑

The decision for every pipe has to pursue two ojectives:

[𝐵𝑗 , ത𝐵𝑗]Maximize benefit

Minimize cost ൧[𝑐𝑗𝑡; ҧ𝑐𝑗

𝑡

81

Proposed method






optimization


82

Risk Assessment: Output

Pareto front of most

critical maintenance items

Item 3

Item 56

Item 72

Item 101

…

…

…

Yes

No

Yes

Yes

No

No

Yes

…

How to select maintenance

porfolios?

Example of

portfolio of actions

2𝑁possible

binary

portfolios of

actions !

Benefit

Cost

Benefit

Cost

Benefit

Cost

Benefit

Cost

83

Portfolio Decision Analysis

Objective: Identification of efficient inspection portfolios, i.e.

a portfolio is efficient if no other feasible portfolio gives a higher overall benefit at

a lower cost.

RPM: linear programming optimization technique, handling interval-valued

objective functions and alternative interdependencies

84

Application

• Large sewerage network in Espoo,

Finland

• More than 33000 sewer pipes, for a

total length of about 900 km.

• Analysis of a subset of 6103

selected pipes, whose past

inspection outcomes are recorded.

85

Results: Step 1

First Pareto frontier:

2079 pipes

Failure SeverityClass 1

Class 2

Class 3

Pipe 3

Pipe 56

Pipe 72

Pipe 101

Pipe 235

Pipe 367

Pipe 461

…

86

Results: Step 2

NUMBER OF

PORTFOLIOS

RUNNING TIME

(MINUTES)

RPM 2000 30

Need for reducing the

uncertainty in expert

estimations

87

•A risk-based approach has been developed to optimize pipeinspection campaigns on large underground networks in thepresence of imprecise knowledge.

•The division of the methodology into three steps allowsreducing the computational effort to select efficient inspectionportfolios.

•The integrated methodologies allow rigorously accommodatingimprecise expert statements.

•Espoo water system case study shows the feasibility of theapproach.

Conclusions

« maintenance · risk-based maintenance (rbm) • basic idea: risk is the criterion for the basis...

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